Geneseo Mathematics Colloquium Schedule

Spring 2010

Game: SET - Math

SET is a popular game for many student math groups (including PRISM). In this talk, we will see many good reasons for this. From a simple game enjoyed (and excelled) by children, we will find geometry (the fourth dimension), topology (tori), algebra, probability, and combinatorics. Aside from all of this, there will be times to play along, and takeaway prizes.

Probabilistic Algebra and Number Theory

At the beginning of my talk I plan to give an intuitive explanation of how to find the probability that 2 integers are relatively prime. This should be interesting and quite accessible to any student who has taken Calculus 2. Next I plan discuss some related explicit examples from my recent joint work with R. Kravchenko and M.Mazur posted at http://arxiv.org/abs/1001.2873. For this part of my talk I will assume that the audience knows matrix and modular arithmetic.

The Mathematics of Your Lifetime: Mathematical Advances of the Last and Next 20 Years

Throughout our mathematical training from elementary school through the first few years of college, we're taught mathematics as facts and ideas that were invented or discovered by people hundreds or even thousands of years ago. This makes it easy for us to think of mathematics as being complete, as if there's nothing left to uncover or create. The reality is that we live in a wonderfully exciting time of mathematical innovation and development, and new breakthroughs are occurring almost daily. In this presentation we will look back at some of the most exciting mathematical developments of the last 20 years - from the solutions of centuries-old problems in pure mathematics like Fermat's Last Theorem and the Poincare Conjecture to mathematical transformations of applications such as medical imaging and quantum computing - and we'll look forward to the possible advances that today's students will have the opportunity to make in the next 20 years.

Level/Background Required: This talk is aimed at any college students with an interest in mathematics. A first course in calculus will be helpful, but no prior knowledge of the problems discussed will be assumed.

Scaling Games to Epic Proportions

An important aspect of computer games is the artificial intelligence (AI) of non-player characters. Currently in games, developers or players can create complex, dynamic behavior for a very small number of characters. However, neither the game engines nor the style of AI programming enables intelligent behavior that scales to a very large number of non-player characters; the languages that define character logic are typically very expensive to process.

In this talk, I will show how solve this problem by modeling game AI as relational queries. Instead of processing characters independently, we can combine all of their behaviors into a single logical query which can then be optimized. The talk will include an overview of the formal framework for specifying character behavior, as well as highlight some of the mathematics behind the ways that we optimize this behavior.